Spontaneous rotation and propulsion of suspended capsules in active nematics

Abstract

We investigate the dynamics of elastic capsules suspended in two-dimensional active nematic fluids using lattice Boltzmann simulations. The capsules, modeled as flexible membranes enclosing active internal regions, exhibit a rich variety of behaviors shaped by their geometry and the interplay between internal and external activity. Circular capsules with active interiors undergo persistent rotation driven by internally confined +1/2 topological defects. Axisymmetric capsules, such as boomerangs, develop directed motion along their axis of symmetry due to unbalanced active forces generated by defect distributions near their boundaries. We further show that capsule flexibility suppresses motility and rotation, as active stresses are dissipated into shape deformations. These findings reveal how shape, deformability, and defect dynamics cooperate to produce emergent motility in soft active matter, with potential applications in the design of microswimmers and drug delivery vehicles.

Figures (4)

• Figure 1: Spontaneous rotation of circular capsules. (a) Fields around capsules of different sizes. From left to right: director field (lines) and charge density (colors) at different times; time-averaged charge density; and streamlines for the time-averaged velocity field, where the color represents its magnitude. The time-averages follow the orientation of the capsule SM. (b) Time evolution of the total angle of rotation for capsules with different sizes. The capsule "s25" represents a solid capsule with $D=25$. (c) Mean squared angular displacement versus time for capsules of different sizes. Two slopes are indicated as a reference. The inset indicates the slope of the curves as a function of the diameters.
• Figure 2: Directed motion of capsules with different shapes along their axis of symmetry. (a) Fields around capsules of different shapes. From left to right: director field (lines) and charge density (colors) at different times; time-averaged charge density; and streamlines for the time-averaged velocity field, where the color represents its magnitude. The averages follow the capsule orientation SM. The arrows indicate the symmetry axis of the capsules, $\mathbf{e}_d$. (b) Capsule velocity along its symmetry axis for the different shapes indicated in "c". The last one is for a solid capsule with boomerang shape. The dashed lines indicates the zero. (c) Histogram of the angle between the velocity field and the symmetry axis for the different shapes: circle, triangle, boomerang and solid boomerang. (d) Mean squared displacement in the direction of the symmetry axis ($MDS_d$) and mean squared angular displacement (MSAD) versus time for different shapes. Two slopes in each plot are indicated as a reference.
• Figure 3: Flexible boomerang-shaped capsules of size $D=25$. (a) Time evolution of the shape of capsules with different stiffness. (b) Time evolution of the mean squared displacement along the capsule symmetry axis for different values of stiffness. Two slopes are indicated as reference. (c) Slopes of the curves as a function of the stiffness.
• Figure 4: Flexible circular capsules of size $D=25$. (a) Time evolution of the shape of capsules with different stiffness. (b) Time evolution of the mean squared angular displacement for different values of stiffness. Two slopes are indicated as reference. (c) Slopes of the curves as a function of the stiffness.